Answer:
Below in bold.
Step-by-step explanation:
Using the quadratic formula :
roots = [-16 +/-√(16^2 - 4*16*5)] / (2*16)
= -0.5 +/- √(-64) /32
= -0.5 +/- 8i/32
= -0.5 + 0.25i and -0.5 - 0.25i
[tex]\sf\longmapsto 16x^2+16x+5=0[/tex]
[tex]\sf\longmapsto x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\sf\longmapsto x=\dfrac{-16\pm\sqrt{16^2-4(16)(5)}}{2(16)}[/tex]
[tex]\sf\longmapsto x=\dfrac{-16\pm√256-320}{32}[/tex]
[tex]\sf\longmapsto x=\dfrac{-16\pm√-64}{32}[/tex]
[tex]\sf\longmapsto x=\dfrac{-16\pm8i}{32}[/tex]
[tex]\sf\longmapsto x=\dfrac{-2\pm i}{4}[/tex]
[tex]\sf\longmapsto x=\dfrac{-1}{2}\pm\dfrac{1}{4}i [/tex]
A triangle has a height of 6mm and an area of 27mm2. What is the length of the base of the triangle?
Answer:
9 mmStep-by-step explanation:
A triangle has a height of 6mm and an area of 27mm2. What is the length of the base of the triangle?
----
To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.
We use the inverse formula
base = 2A : height
2 * 27 : 6 = 9
------------------------
check
6 * 9 : 2 = 27
the answer is good
Two sailboats started at the same location. Sailboat A traveled 5 miles west, then
turned 29° toward the north and continued for 8 miles. Sailboat B first went south
for 8 miles, then turned 51° toward the east and continued for 5 miles. Which
sailboat was farther from the starting point? Explain your reasoning.
The given question can be solved by applying the cosine rule. Therefore, Sailboat A is 12.61 miles away from the starting point. Thus it is the farthest from the starting point.
a. To determine the distance of sailboat A from the stating point.
Applying the cosine rule to the path traveled by sailboat A, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ
= [tex]5^{2}[/tex] + [tex]8^{2}[/tex] - 2(5*8) Cos (180 - 29)
= 25 + 64 -80 * -0.8746
[tex]c^{2}[/tex] = 89 + 70
[tex]c^{2}[/tex] = 159
c = [tex]\sqrt{159}[/tex]
= 12.6095
Thus, the distance of sailboat A from starting point is 12.61 miles.
b. To determine the distance of sailboat B from the stating point.
Applying the cosine rule to the path traveled by sailboat B, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ
= [tex]8^{2}[/tex] + [tex]5^{2}[/tex] - 2(5*8) Cos (180 - 51)
= 64 + 25 -80 * -0.6293
[tex]c^{2}[/tex] = 89 + 50.344
= 139.344
c = [tex]\sqrt{139.344}[/tex]
= 11.8044
c = 11.80 miles
Thus, the distance of sailboat B from starting point is 11.80 miles.
Comparing the distances of the sailboats from the starting point, sailboat A is farther from the starting point.
A sketch is attached to this answer for better reasoning.
Visit: https://brainly.com/question/22699651
what is the vertical asymptote for this function?
y=1/x-2
Answer: x = 0
Step-by-step explanation: so x = 0 is the equation of the vertical asymptote, and 0 must be left out of the domain: (−∞,0)U(0,∞) in interval notation.
Answer:
2
Step-by-step explanation:
what is point W( 7, -4) reflected over the x-axis
Answer:
(7, 4)
Step-by-step explanation:
In this case, where we reflect W(7, -4) over the x-axis, the x-coordinate of the reflection is the same: 7. But the -4 becomes +4 through this reflection.
Reflected point is (7, 4)
8) What are the measures of angles x, y, and z?
Step-by-step explanation:
y=55°(corresponding angles are equal)
x=55°(alternate angles are equal).
z+55°=180°
=180-55=z
z=125°
Answer:
x = y = z = 55°
Step-by-step explanation:
x = 55° (vertical angles)
y = 55° (corresponding angles)
z = 55° (corresponding with x -> z = x)
Eli is following this recipe to bake bread rolls.
He uses 500 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
400 g flour
6 g salt
8 g yeast
40 mL oil
360 mL water
Answer:
7.5 g salt
10g yeast
50 ML oil
450 ML water
Step-by-step explanation:
You would do 1/4 of the amount of (insert ingredient amout) added to the total (insert ingredient amount)
TJ wants to sell his antique 1966 Mustang. He begins to set his price by looking at ads and finds these prices: $12,000, $9,500, $7,500, $14,000, and $12,000. What is the mean, median, mode, and range price?
Answer:
Range: 6,500
The difference between the largest and the smallest number.
Mode: 12,000
The number that appears most.
Mean: 11,000
Because its the average of all numbers
Median: 9,500
The middle number
A temperature of -3°F is how many degrees below the freezing
temperature of water?
Answer:
Step-by-step explanation:
6
I am stuck on a geometry lesson. It is on the Angle Sum Theorem. It said we have an obtuse trisngle with angles 1, 2, and 3. Then they extend the line out as a dashed line top and bottom parallel to each other. It then he says we have angle 1 value would also be true on the opposite side of the triangle like as a transeversal intersected 2 parallel lines making those angles alternate interior angles. He does the sme with 2. then says 1 plus 2 plus 3 equal 180 and says it twice. What does that mean?
What is the area of this tile?
Answer:
Area: 9 in.²
Step-by-step explanation:
Area of square: side²
=> Area of Square tile: 3²
=> 9 in.²
Hoped this helped.
Answer:
9
Step-by-step explanation:
To find the area of a square, multiply both sides.
3*3=9
32is 0.2% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 32, slightly less than , slightly greater than 32, or a lot greater than 32 ? Explain
Answer:
A lot greater
Step-by-step explanation:
32 is 0.2% of the number, that is a small amount compared to what the whole is
Which Game Is The Best And Why?
A.) Uncharted 4 a Thief's End
B.) Call Of Duty Modern Warefare
C.) Batman Arkham Knight
D.) Marvel's Spider-Man
Answer:
Hmm, id say call of duty, because first of all, my brother would not be happy if i chose something else, lol, also that one is pretty fun
Step-by-step explanation:
Darryl can travel to the store on his skateboard three times faster than he can return carrying his package and skateboard. If the total trip takes 30 minutes, how many minutes does it take him to return from the store?
48Step-by-step explanation:
40 = 48 quarts
Geometry- Solve the portion. Question#3
Answer:
[tex]a=1[/tex]Step-by-step explanation:
First let's put our equation[tex]\frac{1}{a+3}=\frac{4}{16}[/tex]Cross - Multiply[tex]4a+12=16[/tex]Subtract both sides by 12[tex]4a=4[/tex]Divide both sides by 4[tex]a=1[/tex]Answer:
a=1
Step-by-step explanation:
Hi there!
We are given the proportion [tex]\frac{1}{a+3} =\frac{4}{16}[/tex], and we want to solve it for the variable, a
Before we start, we can simplify 4/16 to 1/4, since 4 is the GCF of the numerator and denominator of that fraction. Simplifying the fraction will make the computation easier, as the numbers are smaller.
Therefore, the proportion will now be:
[tex]\frac{1}{a+3} =\frac{1}{4}[/tex]
Because this is a proportion, we can cross multiply in order to solve for a; to do that, multiply a+3 by the expression that is on the top right (in this case, 1). Also multiply 4 by the expression that is on the top left (in this case, 1). Then, set them equal to each other, since it is still an equation :)
1(a+3)=4(1)
Multiply
a+3=4
Subtract 3 from both sides
a=1
Hope this helps!
Help please! I do not understand
If Marlene can type 157 words per minute how many words can she type in 25 minute
Answer:
3925
Step-by-step explanation:
25x
25*157
Find the values of x and y, and z
Answer:
z = 15
y = 8
x = 7
Step-by-step explanation:
All of the angles added together equal 180.
4z + 4z + 4z = 180
z = 15
3y - 1 = 23 ( all sides equal each other because all angles equal each other )
y = 8
2x + 9 = 23 ( similar to how I found y )
x = 7
I hope this helps!!
A restaurant keeps eggs in a rack that has 5 layers each layer has 5 row with 5 eggs in each row
Complete the blanks in the materials list to find the total cost of the plumbing fixtures. The quantity of needed items is listed you have to figure the total cost of the materials for the job.
Answer:
$3,466.12 Hope this helped.
Write an equation in slope-intercept form of the line please help me
Answer:
The formula is generally represented equationally as ( y - Y1 ) = m( X - X1 ) so now let's substitute the points plotted on the graph.
it is equal to (y - 4) = m(x - 0)
and now we look for the slope
m = y2 - y1/ x2 - x1
which can be directly substituted according to every line connecting each x value to a certain y value.
$1,000 invested at 8% compounded semiannually after a period of 2 years
Answer:
1160 will be the new amount after 2 years
Step-by-step explanation:
P = $1000, t = 2 years, r = 0.08.
A = 1000(1+0.08(2)) = 1000(1.16) = 1160
Therefore 1160 is the new amount after two years.
Please answer without a link.
Answer:
D) 15/4+5.4
Step-by-step explanation:
The length of a rectangular room is 20 times longer than the width . If the perimeter is 588, what are the dimensions of the room
Answer:
im a teacher sorry not giving answer only hint
explanation:
To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides. This number divided by 2 is the width.
thank you
The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?
Answer:
7 and 1 / 2
Step-by-step explanation:
xy = 9
( 1 / x ) = 4 ( 1 / y )
y = 4x
x ( 4x ) = 9
4x^2 = 9
x = 3 / 2
( 3 / 2 ) y = 9
y = 6
6 + ( 3 / 2 ) = 7 and 1 / 2
The two numbers are 3/2 and 6.
What are reciprocal numbers?The reciprocal of a number is this fraction flipped upside down.
Given that, The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number.
Let the numbers be a and b.
ab = 9.......(i)
1/a = 4/b
a = 4b..........(ii)
Using (i) in (ii)
4b×b = 9
b² = 9/4
b = 3/2
a×3/2 = 9
a = 6
Hence, The two numbers are 3/2 and 6.
For more references on reciprocal numbers, click;
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Sue has 18 3/4 cups of sugar Each pie calls for 1 1/2 cup of sugar Sue wants to break 12 pies Does she have enough sugar How much will be left over or how much more does she need
Answer:
she will have 3/4 cups left over
Step-by-step explanation:
1 1/2 times 12 is 18
find the sum
(2x+6)+(4x-12)
HELp
Answer:
6x - 6
Step-by-step explanation:
(2x + 6) + (4x - 12) ← remove parenthesis
= 2x + 6 + 4x - 12 ← collect like terms
= (2x + 4x) + (6 - 12)
= 6x + (- 6)
= 6x - 6
Twenty-nine lots of p=
Answer:
29p
Step-by-step explanation:
pretty simple
Answer:
29p
Step-by-step explanation:
you
take
p
multiply
by
29
and
the
answer
is
29p
2. Which statement is true? (1 point)
O All quadrilaterals are rectangles.
O All quadrilaterals are squares.
O All rectangles are quadrilaterals.
O All quadrilaterals are parallelograms.
Answer:
the third one
Step-by-step explanation:
all rectangles have 4 sides therefore a quadrilateral
Answer:
3
Step-by-step explanation:
Rectangles require 4 sides and 90 degree corners, a quadrilateral requires 4 sides. So rectangles fulfill the quadrilateral's condition, but quadrilaterals can't always fulfill other forms' condition.
The triangle below models a section of the supports you might see in a construction crane.
a. What is the sum of the angle measures of the triangle? Show your work.
1. Alt interior = 60
2. angle A + angle B + 2 =180
3. x supplemental
4. Alt interior = 90
5. Supplimentary = 90
(A is already solved)
b. Check your answer to problem 3a. Show your work.
(Please answer b)
Exactly what was your answer for a
a woman is 16 weeks pregnant with her first baby. she asks how long it will be before she feels the baby move
It will take about 1 month or 2 months for the baby to start moving since a pregnancy takes 9 months so the most logical thing is that the baby starts to move between 1 month or 2 months